GB1566805A - Counteracting the effects of vibration in beam balances and the like - Google Patents
Counteracting the effects of vibration in beam balances and the like Download PDFInfo
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- G—PHYSICS
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- G01G—WEIGHING
- G01G23/00—Auxiliary devices for weighing apparatus
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Description
(54) COUNTERACTING THE EFFECTS OF
VIBRATION IN BEAM BALANCES AND
THE LIKE
(71) We, METTLER INSTRUMENTE AG, a Body Corporate organised and existing under the laws of Switzerland, of CH-8606 Greifensee, Switzerland, do hereby declare the invention, for which we pray that a patent may be granted to us, and the method by which it is to be performed, to be particularly described in and by the following statement:- This invention relates to counteracting the effects of vibration in beam balances and the like.
The ordinary beam balance is subject to a multitude of error-producing factors that have a detectable effect upon its ability to make accurate weighings; and, for the most part, the more sensitive the balance, the greater the influence these errorproducing factors have upon it. Needless to say, the elimination of these errors has occupied the attention of many skilled scientists for centuries.
These error-producing factors can be considered as falling into two categories, the first of which relates to the mechanism itself and includes such things as friction, parallax, physical characteristics of the components, wear, geometry of the system, capacity, range, etc. The second category, on the other hand, deals with error-producing factors external to the system. Included among the errorproducing factors in this second category are such things as air currents, temperature, humidity, pollutants, characteristics of the sample, static electricity, magnetism and, probably most significant of all, vibration.
The prior art attempts at eliminating the error-producing effects of vibration can be further subdivided into two subclasses, namely those designed to prevent the vibrations from ever reaching the system and those' intended to eliminate or compensate for those that do get through. In the first subclass we find such selfevident solutions as selecting a location for the unit which has a relatively stable environment. Add to this mounting of the unit upon a massive base and one will have done about as much as can be done to isolate the unit from outside influences of this type. In the second subclass, the most common approach to the reduction or elimination of the vibratory forces that do get through to the system is some sort of filter.
Filters provide quite an effective way of nullifying the effect of errorproducing vibrations. However, in so doing, they introduce certain serious complications which, to a large measure, offset their advantages. Probably one of the most serious disadvantages is that of slowing down the time interval that it takes to complete a weighing. The reason for this is that the filtering mechanism must, of necessity, be able to discriminate between a unidirectional force represented by the mass being weighed and the reversible cyclic forces produced by vibrations that are to be ignored. In other words, any functionally adequate filtration system must include some means for distinguishing between those forces acting upon the system that must be included within the final reading and those that are to be eliminated therefrom.Practically speaking, it is the change in the direction of the unwanted forces that can be sensed most easily and which provide the best and most reliable clue to those that should be ignored. Unfortunately, to do this, a time interval must be allowed to elapse during which any and all of the unwanted error-producing vibratory forces will surely have had an opportunity to change direction. This, of course, slows down the weighing procedure appreciably and is a serious disadvantage in many applications.
The unfiltered system is unstable under the influence of vibratory forces and, to whatever extent the case or frame supporting the beam is angularly accelerating relative thereto under the influence of such forces, the output or reading will fluctuate. This is most easily understood in terms of a balance beam which reaches a state of equilibrium at some angle relative to its supporting structure that bears a known relationship to the mass of the sample being weighed. In the simplest form, the beam is provided with a pointer that sweeps across a calibrated scale on the frame thus providing a visual indication of the weight of the unknown mass.If, however, external angularly-directed vibratory forces are at work on the beam supporting structure tending to angularly-accelerate same relative to the beam itself which, because of its inertia, tends to remain stationary in space, then the pointer is going to fluctuate from side-to-side on the scale in direct proportion to the magnitude of such forces.
In fact, all beam-type balances function on the principle of measuring the position of the beam relative to the frame supporting it as in the simple example just given. For instance, in a deflection type balance like that of the foregoing example, the tilt of the beam relative to its frame or support is measured and provides a direct indication of the weight of the unknown mass. Conversely, in what is known as a "virtual motion type balance", the beam actually remains in, or is at least restored to, a fixed position relative to its support while the force required to keep it there is measured and provides the indication of the weight of the unknown mass.Thus, in all beam-type balances, the frame mounting the beam moves in response to angularly-directed forces transmitted to it from the support upon which the frame rests while the beam itself tends to remain stationary in space due to its inertia. The ultimate effect of this angular acceleration of the frame tiltably supporting the beam relative to the beam itself is, as previously mentioned, to produce an unstable condition that is reflected in a fluctuating output or reading.
According to the present invention there is provided a device including a rigid frame, a beam supported by the frame for tilting movement about a horizontal axis that is displaced to one side of its center of gravity at a distance effective to produce a condition of substantial imbalance therein, and means to prevent relative angular motion of the beam and frame due to angular vibratory movement of the frame caused by angular acceleration applied to the frame, said preventing means comprising: a counterweight sized to offset the condition of imbalance in the beam and restore same to an equilibrium position under static no-load conditions and mounted upon or connected to the frame for tilting movement relative thereto about an instantaneous axis of rotation parallel to the axis of tilting movement of the beam; and hanger means operatively connecting said beam and counterweight together for co-ordinated tilting movement relative to one another, the center of gravity of the counterweight being disposed between the point of attachment of the hanger means to the beam and the axis of tilting movement of the counterweight, the points of attachment of said hanger means to said counterweight and to said beam being spaced from their respective axes of pivotal movement at such distances, the mass of said counterweight being such, and the direction in which said counterweight tilts relative to the beam and the moments of inertia of said beam and counterweight about their respective centers of gravity being such, that angular movement of the beam in a sense to nullify substantially all relative angular motion between said beam and frame occasioned by angular vibratory movement of the frame is produced.
The preventing means not only negates the effect of angularly-directed forces due to angular acceleration but, at the same time, does so instantaneously and without having to wait to see if they change direction. Accordingly, in the case where a device in accordance with the invention is a balance, the frequency at which weigaings can be made is limited only by the design of the beam and frame without reference to the preventing means by means of which the effects of vibrational forces tending to angularly move the frame relative to the beam are neutralized and eliminated.
In an embodiment of the invention described below the center of gravity of the counterweight is located halfway between points at which it is suspended, i.e. at the counterweight's center of gravity. However, this is not essential: the location of the center of gravity of the counterweight can be displaced horizontally nearer to one suspension point than the other. In fact, surprisingly, the center of gravity of the counterweight can even lie above or below a straight line defined by the suspension points provided that an offsetting displacement of the center of gravity of the beam off the line defined by the axis of rockable movement thereof and the suspension point of a pan of the balance is introduced into the system.While there is no advantage whatsoever in doing this, nevertheless, it can be done without changing the nullifying effect of the counterweight upon the effects of the said angularly-directed forces.
While the invention is primarily intended to nullify the effects of angular acceleration on the beams of beam balances, it is also equally effective to negate the unwanted consequences arising from the presence of such acceleration in other fulcrum-mounted lever systems such as, for example, phonograph arms or cargo loading booms.
The invention will now be further described, by way of example, with reference to the accompanying drawings, in which:
Figure 1 is a diagram of a conventional double-pan beam balance illustrating linear acceleration forces acting thereon due to vibration;
Figure 2 is a diagram illustrating moments acting about the fulcrum of a typical substitution balance beam
Figure 3 is a diagram illustrating the movement of a frame tiltably mounting a typical beam balance due to the angular acceleration of the supporting surface upon which it rests;
Figure 4 is a schematic diagram of a balance in accordance with the invention showing the suspension of a "Yo-Yo type" counterweight between a beam and a beam-supporting frame of a beam balance;;
Figure 5 is a schematic diagram similar to Figure 4, except that the "Yo-Yo type" counterbalance system has been replaced by a fulcrum-mounted counterweight hanging from a single stirrup;
Figure 6 is a schematic diagram similar to Figures 4 and 5, but differing therefrom in that an irregular mass is used as the counterweight and its center of mass does not lie halfway between its points of suspension;
Figure 7 is a force diagram for a balance shown in Figure 8; and
Figure 8 is a simplified representation of an actual balance modified to form a balance in accordance with the present invention.
Referring to the drawings and, initially, to the diagram of Figure 1, the letter B represents the beam of a simple two-pan balance having pans P suspended by means of stirrups S from the opposite ends thereof. The beam configuration is such that its center of gravity is located very near the axis of rotation of a center knife edge that defines a fulcrum 0 about which the beam rocks with respect to a frame.
In the deflection type balance shown in the diagram, the center of gravity must be located a short distance underneath the knife edge for proper stability; however, in an electronic null type balance, the center of gravity of the beam may be located precisely at the fulcrum 0. In either case, the balance operates by summing
moments about the fulcrum 0, i.e., a weight (W) in one of the pans (P) produces a
moment equal to the product of the weight and the length of that portion of the
lever arm (I) on the same side of the fulcrum.
Now, if the beam is balanced and the center of gravity of the beam lies precisely on the axis of tiltable movement defined by fulcrum 0, no linear acceleration component of the frame, due to vibration of the frame, that acts vertically (at), i.e., perpendicular to the axis of tiltable movement or horizontally, i.e., at right angles to said axis (ax) or parallel thereto, (ay) will produce a moment on the beam B about the fulcrum 0. Thus, the stability of the balance reading remains unaffected by any of the foregoing linear acceleration components or any combination thereof.Using a configuration like that illustrated in the diagram of
Figure 1, therefore, a beam weighing several hundred grams can be used to make weighings in the microgram region without being affected by linear acceleration of the frame supporting same vertically or in a horizontal plane.
Angular acceleration of the supporting frame mounting the beam B is,
however, another story because the balance beam does have inertia and, for this
reason, it tends to remain stationary in space independent of rotation of the frame.
The diagram of Figure 2 to which reference will now be made is illustrative of a
balance beam B having parameters characteristic of those found in a conventional
substitution balance.
The moment of inertia of this simplified beam system (IB) about the axis of
tiltable movement thereof defined by fulcrum 0 can be stated mathematically as
follows:
Equation (1) IB=M,112+M2122=45 gm. cm. sec.2 where
lt =7 cm.
12=14 cm.
M1g=300 grams
M2g=150 grams
Suppose that the frame is subject to an angular vibratory force such that, with respect to the frame, the beam is subjected to an angular acceleration (a). Such acceleration can be considered equivalent to applying a moment to the beam, the moment being given by:
Equation (2) M=IBa where
a is the angular acceleration in radians/sec.2
Now, if the beam moment induced by a pan weight of, say, one milligram is made equivalent to the moment due to a particular angular acceleration of the beam (a,), then this angular acceleration can be calculated as follows::
M (1x10-3 gm) (7 cm)
Equation (3) a=-= =l.55x l0- rad/sec2
IB 45 gm. cm. sec.2
This is the amount of angular vibratory acceleration which, when applied to the beam, will produce +1 mg. variation in the balance reading. This amount of angular acceleration is somewhat difficult to comprehend. However, it can be made more meaningful if it is related to frequency and displacement which can easily be done by means of Figure 3 to which detailed reference will now be made.
Figure 3 is intended to represent a right end view of a typical balance case C resting atop a vibrating supporting surface or table T. Case C, of course, forms a part of the beam-supporting framework and any angularly-directed forces effecting it result in the type of relative angular movement between the beam and the frame that the present invention is intended to eliminate. More specifically, an angular acceleration of the table T will produce a corresponding acceleration of the frame which can be considered to be a corresponding acceleration of the beam with respect to the frame.If the table is undergoing angular acceleration (a;), the vertical displacement of the rear balance feet (m) can be calculated as follows assuming a 60 cycle frequency of vibration which is common to many locations where machinery is being operated from a 60 cycle source of electric power:
Equation (4) α#=1.55x10-4 sin 120 not The angular velocity:
-1.55x10-4
Equation (5) a)6=la,dt= Cos 120 7tt 120 is And the angular position:
-1.55x10-4
Equation (6) OE=Wdt= Sin 120 #t (120 ,r)2 The amplitude of the vertical translation of the balance feet is, therefore: : EQUATIoN( 7)
inches
Even when the output of the balance is filtered through a first order filter having a band pass of 0.6 cycles/sec., the vertical translation of the balance required to produce a +l milligram output flutter is:
EQUATION(8)
inches
Obviously, from equations 7 and 8, it becomes quite apparent that angular acceleration of the beam resulting from angular components of vibratory forces applied to the frame and having an order of magnitude so small as to seem inconsequential in fact have a pronounced effect upon the balance output even using a first order filter.
With the foregoing as background information on the general problem of the effect that the angular acceleration components of vibratory motion have upon fulcrum-mounted lever arms of one type or another, reference will now be made to
Figure 4 wherein a solution to the problem has been illustrated diagrammatically in accordance with the present invention.
In Figure 4, a single-pan counterweight beam balance has been illustrated diagrammatically wherein the counterweight (CW) has a Yo-Yo like configuration and is suspended by a flexible tape (Q) between the beam (B) and an element tiltably mounting said beam and represented by the letter "C". Element C forms a part of the frame mounting the beam and it responds to the angular acceleration components of vibratory motion applied thereto in the manner previously set forth in connection with Figure 3 and, as it does so, there is a relative angular vibratory motion between the beam and said frame unless such movement is otherwise counteracted.
The Yo-Yo like counterweight (CW) can take any one of several forms and still function perfectly well for its intended purpose, the main criteria being that it be suspended for rotation about an axis Ocg that parallels the axis of tiltable movement of the beam (0B). The counterweight (CW) must not be pendulous with respect to its axis of rotation (Ocg) because pendulosity would result in an unwanted counterweight torque due to lateral acceleration.
Of equal importance is the relationship of the tape Q, and particularly the right-hand and left-hand limbs (QR and Q,) thereof, to the counterweight (CW). A groove (G) in the counterweight lies in a plane normal to the axis of tiltable movement of the beam (OB) The groove is circular, is centered on the axis of rotation of the counterweight and has a radius R1. The points of attachment of the right and left-hand limbs (QR and Q,) of the tape to the frame C and beam B, respectively, are selected such that these limbs hang down vertically. This means, of course, that their points of tangency (R and L) with the groove (G) lie spaced apart on a horizontal line passing through the axis of rotation and having a length 2R1 in all angular positions of the counterweight.R1, therefore, becomes the horizontal distance from the axis of rotation (Ocg) of the counterweight (CW) out to one of the points of tangency R or L and this distance must remain the same in all angular positions of the counterweight.
By counterbalancing the beam (B) with the Yo-Yo counterweight (CW) suspended on the tape (Q) as described, the moment on the beam due to angular acceleration can be instantaneously cancelled, whereby relative angular motion between the beam and frame is nullified by virtue of a compensating movement applied to the beam, in the following manner. First, the sum of the moments around the fulcrum 0B can be expressed mathematically as follows:
For static equilibrium:
Equation (9) ZM,=O=M,RR,-IR MgR4 where:
Mp is the mass of the pan, substitution weights, etc; MCW is the mass of the counterweight yo-yo; and
g is the acceleration of gravity.
This equation describes the equilibrium condition of the simplified beam system of Figure 4. It is understood that actual balance systems are more complex but that the Yo-Yo counterweight principle is still applicable.
Equation (9) can be rewritten to give:
R4
Equation (9a) Mp=Mcw 2 R2 Since IB=MP. R23, Equation 9a can be rewritten to give:
Mcw.R2.R4
Equation (9b) IB = MCW. R3. R4
2
When the balance case is subjected to an angular acceleration (a), the force (F,), which is always downward, must decrease or increase by an amount (AF1) as necessary to angularly accelerate the beam by the same amount (Q). So::
Equation (10) AF1 . R4=15a IBQ Equation (11) AF1= R4
The counterweight must be angularly accelerated by the same amount (a) (otherwise the tape Q would fold or tear) by the sum of the forces AF1 and an additional force AF2 corresponding to the rotational acceleration of the frame so that:
Equation (12) (AF2+AF1)R1=Icwa where ICW is the moment of inertia of the counterweight about its center of gravity and is given by:
Equation (12a) Icw=1/2(Mcw- R2)-
Now the center of gravity of the counterweight must be linearly accelerated by the difference of the forces AF2 and AF1 such that::
Equation (13) AF2AF1=McwAv where MCW is the mass of the counterweight;
Av is the vertical acceleration of the center of gravity.
The vertical acceleration Av can be expressed in terms of the angular
acceleration (a) as:
Equation (14) A=(R4+R1)a By combining equations 12, 13 and 14 we have: Icα Mcw(R4+R1)α Equation (15) #F1 = ------ - ------------ 2R1 2
and by combining equations 11 and 15, we obtain the following equation:
Equation (16) Ie Icw MCWR4 M,WRI R4 2R1 2 2
It should be understood that Equation (16) is valid only for the simplified beam of Figure 4. For actual balance configurations it will be necessary to account for total beam inertia.
By simplifying Equation (16) through substitution of the values for IB and ICW taken from Equations (9b) and (12a) we have the following equation representing the characteristics of the counterweight (CW) necessary to counteract the angular movement of the beam produced by the angular acceleration component applied to the beam;; R22-2 R1R4-2R21
Equation (17) R3= 2 R1
Thus, if the Yo-Yo counterweight is designed so that its major and minor radii (R2 and R1) are related to the balance beam lengths (R3 and R4) as indicated in
Equation (17), the moment that can be considered applied to the beam by virtue of the angular acceleration will be completely cancelled by an opposite moment applied to the beam by the counterweight or, in other words, the angular movement of the beam with respect to the frame caused by angular acceleration of the frame due to vibration of the frame will be completely cancelled by an opposite movement applied to the beam by the counterweight.
In use of the Figure 4 system, there is a combination of three types of movement which occur simultaneously:
(a) vertical displacement of the counterweight (CW) due to the vertical acceleration A,; (b) rotation of the counterweight about its center of gravity due to the difference between F1 and F2; and
(c) tilting of the counterweight about an axis OR parallel to the axis OB. where the limb QR of the tape is tangential to the counterweight.
The sensitivity of a beam balance to angular acceleration is directly proportional to the ratio of beam system moment of inertia divided by the display resolution of the balance. That is to say, a balance with high display resolution will be more sensitive to disturbances than a balance with low display resolution. In other words, angular acceleration will have a pronounced effect upon the stability of a balance with a massive beam that is capable of reading in the microgram region while it may not be noticeable in a balance with a low moment of inertia sensitive only to a tenth of a gram.
The Yo-Yo counterbalance will, due to certain fixed errors, require correction. However, adjustments can be made to compensate therefor, either by trial and error or by introducing a correction factor thus providing perfect correction with the beam system in equilibrium, i.e. with no weight on the pan. In the case where a Yo-Yo counterbalance is used and a weight on the pan is electrochemically offset, the Yo-Yo will compensate for angular acceleration of the beam system but not for the unknown added weight. The angular acceleration thus has a residual, uncompensated effect, in this case, the effect being proportional to the mass of the unknown weight and the square of the length of the beam between the pen knife edge and the main knife edge.
In a typical substitution balance, the moment of inertia of the beam system is of the order of 30 gm. cm. sec.2. The effective moment of inertia of the largest unbalanced weight to be used on this balance, on the other hand, would be approximately 0.05 gm. cm. sec.2. In the absence of the angular acceleration compensation mechanism described above, the angularly-directed acceleration forces would act upon the entire moment of inertia of the beam system i.e., 30 gm.
cm. sec.2. However, with such a mechanism included, they act only upon the largest weight which remains uncompensated for, thus making a correction factor approaching 1000 to 1 possible.
Now, the single-pan tiltable beam configuration of Figure 4 is ideally suited for use with the tape-suspended Yo-Yo type counterweight as the latter functions just as well with the beam tilted as it does with it horizontal. The tape Q does not slip with respect to the counterweight. However, there is some friction involved between the tape and the groove in which it sits, namely friction between the sides of the tape and the sides of the groove as well as a minute amount of static friction where the limbs (QR and QL) are tangential to the groove. The friction between the
Yo-Yo and the tape will, in all probability, however, be of sufficient magnitude to render such a counterbalance system unsuitable for accurate weighings of less than a milligram or so.Fortunately, most modern balances do not use a tiltable beam, but instead, a stationary one like that illustrated diagrammatically in Figure 5.
Now, at first glance, the Figure 5 system seems entirely different than that of
Figure 4 in that the modified counterweight (CW') does not rotate about an axis through its center of gravity (cg') but instead, it merely tilts about fulcrums (R' and
L') contained within the confines thereof and which are supported by stirrup Q', and frame C. In reality, however, the counterweight (CW') of Figure 5 and its method of suspension between the beam (B') and frame (C) is nothing more than a special adaptation of the Figure 4 concept applicable only to the so-called virtual motion type balance previously described and partially and diagrammatically represented here by a coil (G) carried by the beam (B') and a magnet (H) operative to restore the beam to its equilibrium position upon the application of currents thereto which are proportional to the load of the unknown mass on the pan P.The -reason for this is that if, in fact, counterweight (CW') were allowed to tilt, fulcrums (R' and L') would no longer lie on a horizontal line and the resolution of these points (R' and L') back onto a horizontal line would result in their being closer together than 2R1 which condition must be present as has already been mentioned.
Accordingly, in the virtual motion system of Figure 5, where, for all practical purposes, the beam does not move, then suspension points (R' and L') stay the same distance apart (2R1) and spaced equidistant on opposite sides of the axis of rotation paralleling the axis of tiltable movement (0t3) of the beam that passes through the center of gravity (cg'). The single remaining stirrup (QT) hangs vertically just like its counterpart QL in the flexible tape system of Figure 4 and were it not for the friction problems created by such a connection, one or both of these stirrups could be replaced by lengths of flexible tape or cord permanently
attached where the knife-edge fulcrums (R' and L') have been shown in the diagram.
In Figure 5, fulcrum (R') becomes an instantaneous center of rotation (our).
By, once again, figuring the forces F1 and F2 acting at points L' and R' (corresponding to points X in limbs QR and QL of Figure 4) it will immediately become apparent that the exact same conditions are present that have already been described in detail in connection with Figure 4. The summation of the moments about the axis of tiltable movement (O'B) still remain as expressed mathematically by Equation 9. Equations 10 through 16, on the other hand, are still valid insofar as expressing the dynamic equilibrium that exists in the system.
Next, with specific reference to Figure 6, the theories advanced with respect to the regularly-shaped counterweights of Figures 4 and 5 will be re-examined with respect to the more general case of an irregular counterbalancing mass to show that they still remain valid. Following this, a general set of relationships can be developed applicable to any shape of counterweight coacting with a fulcrummounted beam system to nullify the effects of angular accelerating forces acting thereon.
If we look at the beam of Figure 6, its moment of inertia (I8) can be shown to be the sum of mass of each particle of the beam (dim,) times the square of its distance from the fulcrum or axis of tiltable movement 0. This can then be expressed as the surface integral (i) thus:
Equation (18) 1B=Yb2 dm, Therefore, regardless of how complex the beam itself is or the various factors that must be taken into consideration in determining its total inertia, the preceding surface integral correctly expresses same.
Now, the moment of inertia of the counterweight (ICW) about an axis passing
through its center of gravity can be expressed mathematically as the sum of the mass of each particle (dim,,) times the square of its distance (RCW) from the center of gravity (ycw) and is thus stated as a surface integral in the following form:
Equation (19) ICw=fRcw 2dim,, In this embodiment, however, the counterweight does not rotate about an axis passing through its center of gravity (yew) but instead, about an instantaneous axis of rotation parallel to the axis of tiltable movement of the beam that is displaced from said centroid by the shortest straight line (perpendicular) distance R,.
Equations (12) to (16) correspond to the special case where the center of gravity of the counterweight (yew) is equally spaced between the counterweight suspension points R and L.
Examining the forces (F1 and F2) applied to the counterweight by the tape QL and frame C, respectively, for equilibrium, we.have Equation (20) F+F2=MCwg where M,mass of counterweight
g=acceleration of gravity
Equation (21) FrR=F2Ro Now by combining equations (20) and (21) we have:
Mcwg R0 Equation (22) F1 = ----- R0+R1 For static equilibrium of the beam:
Mcwg R0 R4 Equation (23) Mp . g R3 = Mcwg R0 R4 R0 + R1 where
R3 is the distance between the pan and beam knife edges.
From equation (23) it is obvious that the beam of Figure 6 is not subjected to angular movement by vertical acceleration since the gravity term (g) divides out of the moment Equation (23). It is evident from Figure 6 that lateral (i.e. horizontal) acceleration will not subject the beam to angular movement provided that the centers of gravity of the counterweight and of the beam are carefully located with respect to the corresponding knife edges suspending them.
If the beam is to follow an angular acceleration (a) about the fulcrum 0 applied thereto by the case, the force AF, necessary in the suspension tape is:
Equation (24) AF, . R4=IBa or Ia
AF1= R4 where
Ig is the moment of inertia of the beam system.
If the counterweight is to follow the angular acceleration (a) two additional
conditions must be met:
Equation (25) #F1R1+AF2R0=Icwα 'where I, is the moment of inertia of the counterweight, and MCW is the mass of the counterweight
Equation (26) AF2-AF1=M(R4+R1)a By combining equations (24), (25) and (26) we arrive at a more general application equation that allows for the situation where the center of gravity of the counterweight is not necessarily at the midpoint of the line between the two attachment points:
Equation (27) IcwR4=I8( RL +RO)+MCWROR4(R1 + R4)
By substituting (R,=RO) into equation (27) we can reduce it to::
Equation (28) I8 lCw MCw(R1+R4) R4 2Rt 2
Equation (28) is in agreement with equation (16), which represents the special case where the center of gravity is at the midpoint between the attachment points.
Having explored the general case exemplified by Figure 6, we are now in a position to identify those relationships necessary in any counterweight arrangement and the suspension system supporting same between the beam and frame that will be effective to cancel such errors in the readout as are occasioned by instability resulting from relative angular movement between the frame and beam. For this purpose, detailed reference will continue to be made to the diagram of Figure 6 wherein these relationships are revealed in their most general terms.
To begin with, the counterweight (CW) is partly suspended by the beam (B) and partly by the frame (C). Attachment points L and R should be on a common line with the center of gravity of the counterweight. The center of gravity (ycw), on the other hand, must be half way in between the attachment points (L and R) (except for virtual motion systems), otherwise various system positions will produce unwanted pendulous conditions which will interfere with the compensating action.
Now, it can be shown that when the distance from the center of gravity (Ycw) to the frame attachment point (R) equals the radius of gyration (RG) of the mass (CW), then relative angular acceleration of the frame (C) with respect to the beam (B) will have no effect whatsoever upon the latter. Furthermore, if the minor dimension (Rg) between the centre of gravity of the mass (CW) and the attachment point R exceeds the radius of gyration (RG) of mass (CW), then the effect of angular acceleration of the frame (C) relative to the beam (B) will be such as to increase rather than reduce its unstabilizing effect upon the latter.Accordingly, the minor dimension (RQ) of the counterweight (CW) must be less than its radius of gyration (RG)- The manner in which the counterweight (CW) is suspended between the beam and frame is, of course, important. The above relationship between the dimension (Ro) and the radius of gyration of the counterweight is valid when both counterweight attachment points (L and R) are on the same side of the central knife edge of the beam. For the case where one counterweight attachment point (say L) is on one side of the fulcrum (0) and the other attachment point (R) is on the other side of flucrum (0) the minor dimension (Ro) must exceed the radius of gyration of the counterweight (CW).
In all instances, beam rotation will bring about a corresponding rotation of the counterweight about an instantaneous axis of rotation within the interior of the mass that is:
(1) Fixed relative to the frame (C);
(2) Parallel to the axis of tiltable movement of the beam ( 8); and
(3) At a perpendicular distance (Ro) from the center of gravity (cow).
Last, but by no means least, the beam moment of inertia must be related to the counterweight moment of inertia according to the general equation (27) which must be modified for different attachment configurations as outlined above.
In Figures 7 and 8, to which reference will now be made, the significant structural features of an actual balance have been shown in two different forms,
Figure 7 being a force diagram while Figure 8 is a schematic. The particular balance used was a Mettler Model HE-lO substitution balance which was modified to constitute an apparatus embodying the present invention in order to evaluate the theories advanced previously. The balance in question is an electronic nullrestoring type unit with a capacity of 160 grams and a sensitivity of 0.0001 grams.
The counterweight CW" had an assymetrical configuration as shown and was connected to a point on the beam on the opposite side of its axis of the tiltable movement "8 by a thin (0.001 inch) stainless steel tape Q",. The frame reference for the counterweight was via a sapphire knife edge R" mounted on the counterweight CW" that was positioned upon a flat sapphire bearing block C' that comprises an element of the main frame.
In order to determine the size of the counterweight CW", it was first necessary to calculate the inertial parameters of the unit which, was done as follows, not all of the elements having been shown in either figure:
Ass'y Description Ass'y Weight Ass'y Moment of Inertia
Pan, stirrup ass'y.,
weight hanger ass'y.,
and weights 262.3 gms. 13.10 gm. cm. sec.2
Aluminum position flag 3.55 0.29
Coil assembly 13.68 2.03
Rear arrestment bar 17.7 1.80
Beam Structure remaining 62.6 2.25
Total Beam Moment of Inertia -- 19.47 gm. cm. sec.2
In Figure 7, it will be apparent that, while the center of gravity (cg") of the counterweight CW" lies on the line interconnecting the two attachment points L" and R", it is no longer midway therebetween so the R'o does not equal R', as was true before.Instead, R't is considerably longer than R'o.
In the foregoing calculation of total beam moment of inertia, no term was included for the conventional beam counterweight (not shown) which was done away with entirely. Now, in order to establish a state of static equilibrium with the standard counterweight removed, it became necessary to construct the counterweight CW" such that the static force in the tape Q", was equal to 200 grams.Since it is highly desirable to utilize as large a spacing as practicable between L" and R", brass was used as the material from which the counterweight was fabricated and it had a total mass (mew) of 0.75 gm. sec.2/cm. Using this figure for MCW along with the aforementioned 200 gram static force rrequirement, Equation 22 can be used to determine the spacing between the points of attachment to the counterweight L" and R" and, more particularly, the distances along line L" R" to the cg", namely, R'o and R" as follows:
(Mcw) g R0 F1
R1+RO where
F,=the static tape force of 200 gms.
Mcw=the mass of CW" or 0.75 gm. sec.2/cm.
g=acceleration of gravity at 981 cm/sec.2.
Simplifying the above equation using the values stated, R,=2.68 R0 The counterweight CW" had a more or less square figure 8 shape and its moment of inertia was calculated by subdividing it into a plurality of right parallelepipeds and then combining the moments of inertia of the several subdivisions.This procedure yielded a total counterweight moment of inertia of: I,,"=16.32 gm. cm. sec.2
Now, by substituting the above parameters into the general counterweight application equation (Equation 27), it becomes possible to evaluate the location of points L" and R" with respect to the center of gravity (cg") of CW", as follows:
Equation (27) ICWR4=IB(RO+ R1)+MCWROR4(RA + R4)
The following values were used in the above equation: Icw=16.32 gm. cm. sec.2
I,=19.47 gm. cm. sec.2 Mcw=0.75 gm. sec.2/cm.
R4=6.8 cm.
R,=2.68 R0 This equation (27) reduces to: E+7.78 R0-8.l2=0 or, RQ=.932 cm.
and R,=2.68 R0=2.498 cm.
A squared figure 8 configuration counterweight was fabricated with attachment point spacing fixed according to the above calculations for R, and RO.
It was installed in a Mettler Model HE-10 electronic substitution balance and the following tests were conducted.
The balance thus modified was mounted oh an angular vibration table along with another standard model HE-10 unit for comparison purposes. The angular vibration table was specifically designed to rotate each balance about an axis coincident with the forward (pan supporting) knife edge so as to isolate beam inertial forces from small, yet measurable, pan swing forces. The angular vibration table was drawn by a variable speed motor using an adjustable travel crank and connecting rod. Tests were conducted at several different frequencies, between zero and ten radians/sec. at different amplitudes. In all cases, the amplitude of the output acceleration of the compensated balance as here measured at the units analog output terminal, was reduced by a factor between 100 and 1000 with respect to that of the uncompensated balance.
No attempt was made to tune the counterweight parameters to better the correction ratio; however, it can be assumed that the calculated parameters are not perfect and hence even larger correction factors are possible.
WHAT WE CLAIM IS:
1. A device including a rigid frame, a beam supported by the frame for tilting movement about a horizontal axis that is displaced to one side of its center of gravity at a distance effective to produce a condition of substantial imbalance therein, and means to prevent relative angular motion of the beam and frame due to angular vibratory movement of the frame caused by angular acceleration applied to the frame, said preventing means comprising: a counterweight sized to offset the condition of imbalance in the beam and restore same to an equilibrium position under static no-load conditions and mounted upon or connected to the frame for tilting movement relative thereto about an instantaneous axis of rotation parallel to the axis of tilting movement of the beam; and hanger means operatively connecting said beam and counterweight together for co-ordinated tilting movement relative to one another, the center of gravity of the counterweight being disposed between the point of attachment of the hanger means to the beam and the axis of tilting movement of the counterweight, the points of attachment of said hanger means to said counterweight and to said beam being spaced from their respective axes of pivotal movement at such distances, the mass of said counterweight being such, and the direction in which said counterweight tilts relative to the beam and the moments of inertia of said beam and counterweight about their respective centers of gravity being such, that angular movement of the beam in a sense to nullify substantially all relative angular motion between said beam and frame occasioned by angular vibratory movement of the frame is produced.
2. A device as set forth in Claim 1, wherein the distance between said instantaneous axis of rotation of the counterweight and the center of gravity of the counterweight is less than the radius of gyration of said counterweight.
3. A device as set forth in Claim 1 or Claim 2 in which: ICWR4=IB(Ro+R1)+McwRoR4(R1 +R4) where ICW is the moment of inertia of the counterweight about its center of gravity, IB is the moment of inertia of the beam system about its center of gravity, MCW is the mass of the counterweight,
R4 is the distance separating the axis of tilting movement of the beam from its point of attachment to the hanger means, R0 is the distance separating the axis of tilting movement of the counterweight from its center of gravity, and
R, is the distance separating the center of gravity of the counterweight from its point of attachment to the hanger means.
4. A device as set forth in Claim 1, Claim 2 or Claim 3, wherein the point of attachment of the hanger means to the beam lies on the same side of the center of gravity thereof as its axis of tilting movement.
5. A device as set forth in any one of the preceding claims, wherein the axes of tilting movement of the beam and counterweight are displaced to one side of their
respective centers of gravity so as to define parallel planes.
6. A device as set forth in any one of the preceding claims, wherein the beam and counterweight lie in superimposed relation one above the other, and the points of attachment between the hanger beams and said beam and said counterweight lie in vertically-spaced relation to one another.
7. A device as set forth in any one of the preceding claims, wherein the axis of tilting movement of the counterweight comprises a knife edge bearing.
8. A device as set forth in any one of the preceding claims, wherein the point of attachment of the hanger means to the counterweight lies inside the circle defined by the radius of gyration of the latter.
9. A device as set forth in Claim 8, wherein the axis of tilting movement of the counterweight also lies inside said circle.
10. A device as set forth in any one of the preceding claims, wherein the center
**WARNING** end of DESC field may overlap start of CLMS **.
Claims (19)
1. A device including a rigid frame, a beam supported by the frame for tilting movement about a horizontal axis that is displaced to one side of its center of gravity at a distance effective to produce a condition of substantial imbalance therein, and means to prevent relative angular motion of the beam and frame due to angular vibratory movement of the frame caused by angular acceleration applied to the frame, said preventing means comprising: a counterweight sized to offset the condition of imbalance in the beam and restore same to an equilibrium position under static no-load conditions and mounted upon or connected to the frame for tilting movement relative thereto about an instantaneous axis of rotation parallel to the axis of tilting movement of the beam; and hanger means operatively connecting said beam and counterweight together for co-ordinated tilting movement relative to one another, the center of gravity of the counterweight being disposed between the point of attachment of the hanger means to the beam and the axis of tilting movement of the counterweight, the points of attachment of said hanger means to said counterweight and to said beam being spaced from their respective axes of pivotal movement at such distances, the mass of said counterweight being such, and the direction in which said counterweight tilts relative to the beam and the moments of inertia of said beam and counterweight about their respective centers of gravity being such, that angular movement of the beam in a sense to nullify substantially all relative angular motion between said beam and frame occasioned by angular vibratory movement of the frame is produced.
2. A device as set forth in Claim 1, wherein the distance between said instantaneous axis of rotation of the counterweight and the center of gravity of the counterweight is less than the radius of gyration of said counterweight.
3. A device as set forth in Claim 1 or Claim 2 in which: ICWR4=IB(Ro+R1)+McwRoR4(R1 +R4) where ICW is the moment of inertia of the counterweight about its center of gravity, IB is the moment of inertia of the beam system about its center of gravity, MCW is the mass of the counterweight,
R4 is the distance separating the axis of tilting movement of the beam from its point of attachment to the hanger means, R0 is the distance separating the axis of tilting movement of the counterweight from its center of gravity, and
R, is the distance separating the center of gravity of the counterweight from its point of attachment to the hanger means.
4. A device as set forth in Claim 1, Claim 2 or Claim 3, wherein the point of attachment of the hanger means to the beam lies on the same side of the center of gravity thereof as its axis of tilting movement.
5. A device as set forth in any one of the preceding claims, wherein the axes of tilting movement of the beam and counterweight are displaced to one side of their
respective centers of gravity so as to define parallel planes.
6. A device as set forth in any one of the preceding claims, wherein the beam and counterweight lie in superimposed relation one above the other, and the points of attachment between the hanger beams and said beam and said counterweight lie in vertically-spaced relation to one another.
7. A device as set forth in any one of the preceding claims, wherein the axis of tilting movement of the counterweight comprises a knife edge bearing.
8. A device as set forth in any one of the preceding claims, wherein the point of attachment of the hanger means to the counterweight lies inside the circle defined by the radius of gyration of the latter.
9. A device as set forth in Claim 8, wherein the axis of tilting movement of the counterweight also lies inside said circle.
10. A device as set forth in any one of the preceding claims, wherein the center
of gravity of the counterweight together with its axis of tilting movement and point of attachment to the hanger means are coplanar.
11. A device as set forth in any one of the preceding claims, wherein the hanger means comprises a flexible essentially non-elastic tape which will not elongate appreciably under load.
12. A device as set forth in any one of Claims 1 to 10, wherein the hanger means comprises a rigid stirrup; and, in which the points of attachment between said stirrup and beam and counterweight are defined by knife-edged bearing blocks.
13. A device as set forth in any one of the preceding claims, wherein the counterweight tilts in a direction opposite to that of the beam.
14. A device as set forth in Claim 3, wherein: Rn=R,.
15. A device as set forth in Claim 3; wherein: Ro < R1.
16. A device as set forth in Claim 9 or any claim appendant thereto wherein the counterweight comprises a cylinder having openings on both sides thereof within which are located its axis of tilting movement and the point of attachment of the hanger means thereto.
17. A device as set forth in Claim 16, wherein the counterweight has a Yo-Yo type configuration.
18. A device as set forth in any one of the preceding claims, which is a beam balance.
19. A beam balance substantially as hereinbefore described with reference to any one of Figures 4 to 6 or Figures 7 and 8 of the accompanying drawings.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
GB3309076A GB1566805A (en) | 1976-08-09 | 1976-08-09 | Counteracting the effects of vibration in beam balances and the like |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
GB3309076A GB1566805A (en) | 1976-08-09 | 1976-08-09 | Counteracting the effects of vibration in beam balances and the like |
Publications (1)
Publication Number | Publication Date |
---|---|
GB1566805A true GB1566805A (en) | 1980-05-08 |
Family
ID=10348441
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
GB3309076A Expired GB1566805A (en) | 1976-08-09 | 1976-08-09 | Counteracting the effects of vibration in beam balances and the like |
Country Status (1)
Country | Link |
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GB (1) | GB1566805A (en) |
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
EP0289113A2 (en) * | 1987-02-27 | 1988-11-02 | Yamato Scale Company, Limited | Counterbalanced weighing apparatus |
-
1976
- 1976-08-09 GB GB3309076A patent/GB1566805A/en not_active Expired
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
EP0289113A2 (en) * | 1987-02-27 | 1988-11-02 | Yamato Scale Company, Limited | Counterbalanced weighing apparatus |
EP0289113A3 (en) * | 1987-02-27 | 1989-11-15 | Yamato Scale Company, Limited | Counterbalanced weighing apparatus |
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PCNP | Patent ceased through non-payment of renewal fee |